Question

rationalise the denominator 1/9-3√2

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Answer 1

Step-by-step explanation:

$\frac{1}{9 - 3 \sqrt{2} }$

$\frac{1}{9 - 3 \sqrt{2} } \times \frac{9 + 3 \sqrt{2} }{9 + 3 \sqrt{2} }$

$= \frac{9 + 3 \sqrt{2} }{(9)^{2} - (3) {}^{2} ( \sqrt{2} ) {}^{2} }$

$= \frac{ 9 + 3 \sqrt{2} }{81 - 9 \times 2}$

$= \frac{9 + 3 \sqrt{2} }{81 - 18}$

$= \frac{9 + 3 \sqrt{2} }{63}$